Finally, in view of [1]}, one could expect that in the setting of fractional Brownian motion, the only requirement should be \(Tb \in \mathcal {C}^{\nu }\mathcal {C}^{1}_{w_0}\)  (this is the case when \(\mathbf {w}\)  is the Stratonovitch Brownian rough path). This kind of result would require a use of Girsanov transform as in [2]}, [3]}, [1]}. The bounds of Section  are not good enough, neither the Kolmogorov estimates of Section . Again, we leave this for future investigations.

